Foundations & Economics  (FE) Session 2

Abstract: We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the two-layer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business (layer A) and a more risky subsidiary business (layer B). In such setting a failure (or bankruptcy) on the core layer implies a failure on the subsidiary layer as well, as the failed firm is out of business. On the other hand, a failure on the subsidiary layer only decreases a firm's failure threshold on the core layer and, thus, increases its absolute failure probability in the core business. We show that in most cases, this kind of business diversification may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach. Close

Abstract: Since 2007, several contributions have tried to identify early-warning signals of the financial crisis. However, the vast majority of analyses has focused on financial systems and little theoretical work has been done on the economic counterpart. In the present paper we fill this gap and employ the theoretical tools of network theory to shed light on the response of world trade to the financial crisis of 2007 and the economic recession of 2008-2009. We have explored the evolution of the bipartite World Trade Web (WTW) across the years 1995-2010, monitoring the behavior of the system both before and after 2007. Our analysis shows early structural changes in the WTW topology: since 2003, the WTW becomes more and more compatible with the picture of a network where correlations between countries and products are progressively lost. Moreover, the WTW structural modification can be considered as concluded in 2010, after a seemingly stationary phase of three years. We have also refined our analysis by considering specific subsets of countries and products: the most statistically significant early-warning signals are provided by the most volatile macrosectors, especially when measured on emerging economies, suggesting the latter as the most sensitive indicators of the WTW health. Close

Abstract: Modern societies are often faced to segregation dictated by race, religion, social status or incomes differences. The understanding of the rise of such phenomenon has thus attracted a lot of attention from economists, politicians and sociologists. We first introduce a metapopulation version of the Schelling model showing that an hidden relationship emerges, for low tolerances, between the segregation patterns and the population variability in different urban areas. In particular, we observe that the population frequencies of each node, emerging from the model, once ordered according to the population ranking, follow a Zipf’s law. Motivated by this theoretical result we analyze the internal composition of several metropolitan areas in the US. We show that a universal Zipf’s law is present also at the urban scale and that a correlation between the population heterogeneity and the segregation patterns can be observed. Moreover we analyze the internal urban preferences for different ethnic groups, using the z-score for identifying the overestimation of a certain ethnic group in each zip. We show that density “preferences” can be observed and that the ethnic composition strongly depends on the density. Close

Abstract: We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly) directed spin with the direction of the vector connecting the centers of neighboring disks. The direction of a single spin is controlled by a “temperature”, representing the amount of polarization of the spins in the direction of an external field. Our model is inspired by biological neuronal networks and aims to characterize their topological properties when axonal guidance plays a major role. We numerically study the phase diagram of the model observing the emergence of a giant strongly connected component, representing the portion of neurons that are causally connected. We provide strong evidence that the critical exponents depend on the temperature. Close

Abstract: As human communication datasets become increasingly rich, various approaches have been employed to improve the network modeling in order to uncover hidden aspects of human dynamics. In particular, records of communication events between individuals with high temporal resolutions have enabled us to study dynamical properties of networks rather than static ones, in the emerging field of temporal networks. We study the dynamical properties of human communication through different channels, i.e., short messages, phone calls, and emails, adopting techniques from neuronal spike train analysis in order to characterize the temporal fluctuations of successive inter-event times. We measured the so-called local variation (LV) of incoming and outgoing event sequences of users, which is originally designed to characterize temporal fluctuations in spike train data. We found that these in- and out-LV values are positively correlated for short messages, and uncorrelated for phone calls and emails. An important originality of our work is to focus on the relationship between incoming and outgoing events involving social agents and its impacts on temporal fluctuations. Similarly to neurons, receiving inputs and integrating them to send outputs, social agents are subject to incoming messages that may, or not, trigger reactions. In order to test this idea and to understand the observed LV-correlations, we analyzed the response-time distribution in empirical datasets and developed a generalized Hawkes process to model the observed dynamical properties. Numerical simulations of the model indicate that a quick response to incoming events and a refractory effect after outgoing events are key factors to reproduce the positive LV correlations. This investigation of the input-output relationship in human messaging processes may provide us important insight on how information flows in human communications. Close

Abstract: Flood risk is one of the most frequently occurring disasters worldwide, and cost-benefit analysis is widely applied to assess management strategies. The central number that influences the balance between costs and benefits here is the price of flood risk. It is usually assessed either through the analysis of market-level data using hedonic pricing or by eliciting individual willingness to pay to avoid risk through surveys. The two approaches constitute two different paradigms – micro vs macro – and often produce contrasting results in pricing flood risks. The assessment is also sensitive to the timing after the shock. At the times of natural disasters price trends in flood prone areas shift significantly and abruptly implying that there are systemic changes in property markets. On the one hand, it implies that transactions in the past may not be representative anymore when making current price assessments or projections for the future. On the other hand, it is essential to trace the link between individual risk perceptions and macro-level market outcomes as the former fuel these structural market shifts. This calls for new computation methods for assessing capital-at risk and its fluctuations as shocks occur and markets aggregate individual reactions to these natural hazards. We present an agent-based model of a housing market covering flood prone areas, in which we not only utilize the most recent sales in conducting market price predictions but also explicitly test the evolution of housing prices (and consequently the price of flood risk) emerging from interactions of heterogeneous household agents with various individual representations of risk perceptions. We compare market outcomes under three common behavioral models: expected utility, prospect theory and risk negligence Our results demonstrate non-linearity between agents’ individuals risk perceptions and aggregated price discount, which uncovers the nature of the gap between the two measurement approaches. Close